Heat localization through reduced dimensionality

TL;DR

This paper models how heat localization depends on system dimensionality, showing that low-dimensional systems like nanotubes can achieve extreme temperature gradients, with implications for energy conversion technologies.

Contribution

It introduces a model demonstrating the impact of dimensionality on heat localization and the amplification effect due to temperature-dependent thermal conductivity.

Findings

Heat localization is strongly dependent on system dimensionality.

Low-dimensional systems can reach extremely high temperature gradients.

Thermal runaway can occur when conductivity declines rapidly with temperature.

Abstract

We present a model to show that heat propagation away from a local source depends strongly on dimensionality, leading to dramatic localization in low-dimensional systems. An example of such a system is a carbon nanotube array. We further show that this localization is amplified due to a runaway mechanism if thermal conductivity declines rapidly with temperature. Extremely high temperatures of thousands of Kelvins and gradients of hundreds of K/{\mu}m may thus be obtained in a conductor using a modest local power source such as a laser pointer. This is of fundamental importance for high-efficiency energy conversion through thermoelectric and thermionic mechanisms, as well as various other applications.